Holographic dark energy in a universe with spatial curvature and massive neutrinos: a full Markov Chain Monte Carlo exploration

In this paper, we report the results of constraining the holographic dark energy model with spatial curvature and massive neutrinos, based on a Markov Chain Monte Carlo global fit technique. The cosmic observational data include the full WMAP 7-yr temperature and polarization data, the type Ia supernova data from Union2.1 sample, the baryon acoustic oscillation data from SDSS DR7 and WiggleZ Dark Energy Survey, and the latest measurements of H0 from HST. To deal with the perturbations of dark energy, we adopt the parameterized post-Friedmann method. We find that, for the simplest holographic dark energy model without spatial curvature and massive neutrinos, the phenomenological parameter c < 1 at more than 4σ confidence level. The inclusion of spatial curvature enlarges the error bars and leads to c < 1 only in about 2.5σ range; in contrast, the inclusion of massive neutrinos does not have significant influence on c. We also find that, for the holographic dark energy model with spatial curvature but without massive neutrinos, the 3σ error bars of the current fractional curvature density Ωk0 are still in order of 10−2; for the model with massive neutrinos but without spatial curvature, the 2σ upper bound of the total mass of neutrinos is Σmν < 0.48 eV. Moreover, there exists clear degeneracy between spatial curvature and massive neutrinos in the holographic dark energy model, which enlarges the upper bound of Σmν by more than 2 times. In addition, we demonstrate that, making use of the full WMAP data can give better constraints on the holographic dark energy model, compared with the case using the WMAP ''distance priors''